给您两个平面P1 ： a1 * x + b1 * y + c1 * z + d1 = 0和P2 ： a2 * x + b2 * y + c2 * z + d2 = 0 。任务是编写一个程序来查找这两个平面之间的距离。
例子 ：
Input: a1 = 1, b1 = 2, c1 = -1, d1 = 1, a2 = 3, b2 = 6, c2 = -3, d2 = -4
Output: Distance is 0.952579344416
Input: a1 = 1, b1 = 2, c1 = -1, d1 = 1, a2 = 1, b2 = 6, c2 = -3, d2 = -4
Output: Planes are not parallel 方法：考虑两个平面由等式给出：
P1 : a1 * x + b1 * y + c1 * z + d1 = 0, where a1, b1 and c1, d1 are real constants and
P2 : a2 * x + b2 * y + c2 * z + d2 = 0, where a2, b2 and c2, d2 are real constants.
两个平面平行的条件是：
=> a1 / a2 = b1 / b2 = c1 / c2在任一平面中找到一个点，以使从该点到另一平面的距离成为这两个平面之间的距离。可以使用以下公式计算距离：
Distance = (| a*x1 + b*y1 + c*z1 + d |) / (sqrt( a*a + b*b + c*c))设平面P1中的一个点为P(x1，y1，z1)，
将x = y = 0放在等式a1 * x + b1 * y + c1 * z + d1 = 0中并找到z。
=> z = -d1 / c1
现在我们有了P(0，0，z)= P(x1，y1，z1)的坐标。
点P到平面P2的距离将是：
Distance = (| a2*x1 + b2*y1 + c2*z1 + d2 |) / (sqrt( a2*a2 + b2*b2 + c2*c2))
= (| a2*0 + b2*0 + c2*z1 + d2 |) / (sqrt( a2*a2 + b2*b2 + c2*c2))
= (| c2*z1 + d2 |) / (sqrt( a2*a2 + b2*b2 + c2*c2))
下面是上述公式的实现：
C++
// C++ program to find the Distance
// between two parallel Planes in 3 D.
#include
#include
using namespace std;
// Function to find distance
void distance(float a1, float b1,
float c1, float d1,
float a2, float b2,
float c2, float d2)
{
float x1, y1, z1, d;
if (a1 / a2 == b1 / b2 &&
b1 / b2 == c1 / c2)
{
x1 = y1 = 0;
z1 = -d1 / c1;
d = fabs(( c2 * z1 + d2)) /
(sqrt(a2 * a2 + b2 *
b2 + c2 * c2));
cout << "Perpendicular distance is "
<< d << endl;
}
else
cout << "Planes are not parallel";
return;
}
// Driver Code
int main()
{
float a1 = 1;
float b1 = 2;
float c1 = -1;
float d1 = 1;
float a2 = 3;
float b2 = 6;
float c2 = -3;
float d2 = -4;
distance(a1, b1, c1, d1,
a2, b2, c2, d2); // Fxn cal
return 0;
}
// This code is contributed
// by Akanksha Rai(Abby_akku) C
// C program to find the Distance between
// two parallel Planes in 3 D.
#include
#include
// Function to find distance
void distance(float a1, float b1, float c1,
float d1, float a2, float b2,
float c2, float d2)
{
float x1,y1,z1,d;
if (a1 / a2 == b1 / b2 && b1 / b2 == c1 / c2)
{
x1 = y1 = 0;
z1 =-d1 / c1;
d = fabs(( c2 * z1 + d2)) / (sqrt(a2 * a2 + b2 * b2 + c2 * c2));
printf("Perpendicular distance is %f\n", d);
}
else
printf("Planes are not parallel");
return;
}
// Driver Code
int main()
{
float a1 = 1;
float b1 = 2;
float c1 = -1;
float d1 = 1;
float a2 = 3;
float b2 = 6;
float c2 = -3;
float d2 = -4;
distance(a1, b1, c1, d1, a2, b2, c2, d2); // Fxn cal
return 0;
}
// This code is contributed
// by Amber_Saxena. Java
// Java program to find the Distance
// between two parallel Planes in 3 D.
import java .io.*;
import java.lang.Math;
class GFG
{
// Function to find distance
static void distance(float a1, float b1, float c1,
float d1, float a2, float b2,
float c2, float d2)
{
float x1,y1,z1,d;
if (a1 / a2 == b1 / b2 &&
b1 / b2 == c1 / c2)
{
x1 = y1 = 0;
z1 =-d1 / c1;
d = Math.abs(( c2 * z1 + d2)) /
(float)(Math.sqrt(a2 * a2 + b2 *
b2 + c2 * c2));
System.out.println("Perpendicular distance is "+ d);
}
else
System.out.println("Planes are not parallel");
}
// Driver code
public static void main(String[] args)
{
float a1 = 1;
float b1 = 2;
float c1 = -1;
float d1 = 1;
float a2 = 3;
float b2 = 6;
float c2 = -3;
float d2 = -4;
distance(a1, b1, c1, d1,
a2, b2, c2, d2);// Fxn cal
}
}
// This code is contributed
// by Amber_Saxena.Python
# Python program to find the Distance between
# two parallel Planes in 3 D.
import math
# Function to find distance
def distance(a1, b1, c1, d1, a2, b2, c2, d2):
if (a1 / a2 == b1 / b2 and b1 / b2 == c1 / c2):
x1 = y1 = 0
z1 =-d1 / c1
d = abs(( c2 * z1 + d2)) / (math.sqrt(a2 * a2 + b2 * b2 + c2 * c2))
print("Perpendicular distance is"), d
else:
print("Planes are not parallel")
# Driver Code
a1 = 1
b1 = 2
c1 = -1
d1 = 1
a2 = 3
b2 = 6
c2 = -3
d2 = -4
distance(a1, b1, c1, d1, a2, b2, c2, d2) # Fxn calC#
// C# program to find the Distance
// between two parallel Planes in 3 D.
using System;
class GFG
{
// Function to find distance
static void distance(float a1, float b1,
float c1, float d1,
float a2, float b2,
float c2, float d2)
{
float z1, d;
if (a1 / a2 == b1 / b2 &&
b1 / b2 == c1 / c2)
{
z1 =-d1 / c1;
d = Math.Abs((c2 * z1 + d2)) /
(float)(Math.Sqrt(a2 * a2 + b2 *
b2 + c2 * c2));
Console.Write("Perpendicular distance is " + d);
}
else
Console.Write("Planes are not parallel");
}
// Driver code
public static void Main()
{
float a1 = 1;
float b1 = 2;
float c1 = -1;
float d1 = 1;
float a2 = 3;
float b2 = 6;
float c2 = -3;
float d2 = -4;
distance(a1, b1, c1, d1,
a2, b2, c2, d2);// Fxn cal
}
}
// This code is contributed
// by ChitraNayalPHP
输出：
Perpendicular distance is 0.952579344416